The initial 1D temperature versus depth profile, at the instant when the eruption occurs, can be represented by a piece-wise function: the temperature is a constant T = 15C from d0 = 0m to a depth of d1 = 500m. there is then a sharp transition to a constant temperature of T = 10C from d1 to d2 = 2600m; finally, the temperature at d2 isfixed at T = 380C. The thermal diffusivity of sea-water can be approximated to t = 1.7 102m2/s.

To solve analytically separate your solution into a homogeneous and steady-state solution. It is recommended that you keep your boundary and initial conditions expressed as variables. 1. Using the information given in the Introduction, briefly summarise the problem information. Be sure to include the following:

Governing equation

Order and type of the PDE

Initial condition

Boundary conditions

Type of solution you expect to obtain